標題: | Extracting Computational Entropy and Learning Noisy Linear Functions |
作者: | Lee, Chia-Jung Lu, Chi-Jen Tsai, Shi-Chun 資訊工程學系 Department of Computer Science |
公開日期: | 2009 |
摘要: | We study the task of deterministically extracting randomness from sources containing computational entropy. The sources we consider have the form of a conditional distribution (f(X)vertical bar X), for some function f and some distribution X, and we say that such a source has computational min-entropy k if any circuit of size 2(k) can only predict f(x) correctly with probability at most 2(-k) given input x sampled from X. We first show that it is impossible to have a seedless extractor to extract from one single source of this kind. Then we show that it becomes possible if we are allowed a seed which is weakly random (instead of perfectly random) but contains some statistical min-entropy, or even a seed which is not random at all but contains some computational min-entropy. This can be seen as a step toward extending the study of multi-source extractors from the traditional, statistical setting to a computational setting. We reduce the task of constructing such extractors to a problem in learning theory: learning linear functions under arbitrary distribution with adversarial noise. For this problem, we provide a learning algorithm, which may have interest of its own. |
URI: | http://hdl.handle.net/11536/15840 |
ISBN: | 978-3-642-02881-6 |
ISSN: | 0302-9743 |
期刊: | COMPUTING AND COMBINATORICS, PROCEEDINGS |
Volume: | 5609 |
起始頁: | 338 |
結束頁: | 347 |
顯示於類別: | 會議論文 |